We present an analysis of atmospheric transport impact on
estimating CO2 fluxes using two atmospheric inversion systems
(CarboScope-Regional (CSR) and Lund University Modular Inversion Algorithm (LUMIA)) over Europe in 2018. The main focus of
this study is to quantify the dominant drivers of spread amid CO2
estimates derived from atmospheric tracer inversions. The Lagrangian
transport models STILT (Stochastic Time-Inverted Lagrangian Transport) and FLEXPART (FLEXible PARTicle) were used to assess the impact of
mesoscale transport. The impact of lateral boundary conditions for CO2
was assessed by using two different estimates from the global inversion
systems CarboScope (TM3) and TM5-4DVAR. CO2 estimates calculated with
an ensemble of eight inversions differing in the regional and global
transport models, as well as the inversion systems, show a relatively large
spread for the annual fluxes, ranging between -0.72 and 0.20 PgC yr-1, which is
larger than the a priori uncertainty of 0.47 PgC yr-1. The discrepancies
in annual budget are primarily caused by differences in the mesoscale
transport model (0.51 PgC yr-1), in comparison with 0.23 and 0.10 PgC yr-1 that resulted from the far-field contributions and the inversion
systems, respectively. Additionally, varying the mesoscale transport caused
large discrepancies in spatial and temporal patterns, while changing the
lateral boundary conditions led to more homogeneous spatial and temporal
impact. We further investigated the origin of the discrepancies between
transport models. The meteorological forcing parameters (forecasts versus
reanalysis obtained from ECMWF data products) used to drive the transport
models are responsible for a small part of the differences in CO2
estimates, but the largest impact seems to come from the transport model
schemes. Although a good convergence in the differences between the
inversion systems was achieved by applying a strict protocol of using
identical prior fluxes and atmospheric datasets, there was a non-negligible
impact arising from applying a different inversion system. Specifically, the
choice of prior error structure accounted for a large part of
system-to-system differences.
Introduction
Inverse modelling has been increasingly used to infer surface–atmosphere
fluxes of carbon dioxide (CO2) from observations of dry mole fractions
made at spatio-temporal points across an observational network (Enting and
Newsam, 1990; Bousquet et al., 1999). Reducing uncertainty in the flux
estimates is, therefore, essential to reliably quantify the carbon budget
(Friedlingstein et al., 2022; Le Quéré et al., 2018) as well as
to improve our understanding about the variability and trends of the carbon
cycle over times at finer regional scales, in particular in response to the
climate perturbation caused by the increase in anthropogenic emissions
(Shi et al., 2021). The estimates obtained from atmospheric tracer
inversions still demonstrate large deviations due to manifold sources of
uncertainty such as using different data, inversion schemes, and atmospheric
transport models (Baker et al., 2006; Gurney et al., 2016), either at
global scales or, to a larger extent, at regional scales. Although the
global inversions can provide convergent estimations of the global carbon
budgets, they are limited by the coarse resolution of atmospheric transport
that may not allow for a realistic representation of the observations at
complex mesoscale terrains. In turn, performing regional inversions with
mesoscale transport models has offered a better opportunity to represent and
make use of the dense measurements available at all the sites across
regional domains (Broquet et al., 2013; Kountouris et al., 2018a; Lauvaux
et al., 2016), specifically after the expanding coverage of data over large
areas in recent years as has been established, for example, over Europe
by the Integrated Carbon Observation System (ICOS). Although CO2 fluxes
constrained by atmospheric data in the Bayesian inversion framework inherit
a dominant spatial and temporal pattern from the atmospheric signal, the
a posteriori fluxes still suffer from a large spread when using different
global and mesoscale transport models (Rivier et al., 2010).
As a first intercomparison between six regional inversions covering a wide
range of system characteristics (e.g. prior fluxes, inversion approaches,
and transport models), the EUROCOM experiment (Monteil et al., 2020)
suggested large spreads in posterior estimates over Europe, particularly
over regions that are poorly constrained by atmospheric data. This, on the
one hand, partly indicates the sensitivity of the a posteriori estimates to
the observations and to the a priori models as explained in Munassar et al. (2022). On the other hand, inaccuracies in atmospheric transport (Schuh
et al., 2019), far-field contributions, and the configurations of inversions
are responsible for part of that spread. A further study suggests that
uncertainties in both transport and CO2 fluxes contribute equally to
the uncertainties in CO2 dry mole fraction simulations, displaying
similar temporal and spatial patterns (Chen et al., 2019).
The atmospheric transport relates the measured tracer concentration to its
possible sources and sinks, which are adjusted in order to fit the modelled
concentrations to observed data. However, inaccuracies in representing the
real atmospheric dynamics by transport models lead to uncertainties in
CO2 flux estimates. This kind of error can emerge from both simplified
parameterizations of real physics and model parameters themselves
(Engelen et al., 2002). The atmospheric transport models rely on a mesoscale
representation of air mass movements, which cannot completely reproduce the
observed fine-scale variability of tracer concentration, leading to the
so-called representation error. As a result, inversions cannot solve for
fluxes at lower spatial and temporal resolutions than that of their
transport model, resulting in aggregation errors (Kaminski et al., 2001).
Additionally, atmospheric transport models are typically driven by
meteorological data available from operational weather forecast models or
reanalysis data optimized against observations and dynamical model
forecasts. However, such meteorological fields have uncertainties owing to
errors and gaps in the observations and errors in the weather forecast
models (Deng et al., 2017; Liu et al., 2011; Tolk et al., 2008).
As the lateral boundaries are provided from a global model run at lower
resolution than the regional model (Davies, 2014), this leads to biases
in CO2 lateral concentrations and thus affects the inversion estimates
(Chen et al., 2019). The information of providing boundary conditions to
regional inversions is necessary to isolate the influence of far-field
contributions before performing the regional inversion. In Bayesian
inversion setups, a proper information on prior error structures is also
essential to determine the spatial pattern of the flux corrections based on
the assumed error, especially at high spatial resolution inversions
(Chevallier et al., 2012; Kountouris et al., 2015; Lauvaux et al., 2016).
Therefore, the spatial pattern of flux corrections is dependent on the way
the error covariance matrices are constructed, which can lead to large
spatial discrepancies between the estimates from different inversion
systems.
This study is dedicated to quantify the relative contributions of the
differences in optimized fluxes resulting from varying as follows: (1) atmospheric
transport models, (2) lateral boundary conditions, and (3) inversion
configurations on flux estimates, as the error contributions from each
component to the inversion's spread remain unclear in regional inversions,
specifically at finer spatial scales over a continental domain such as
Europe (Monteil et al., 2020; Petrescu et al., 2021; Thompson et al.,
2020). We analysed results of a posteriori net ecosystem exchange (NEE) estimated from the two inversion
systems CarboScope-Regional (CSR; Kountouris et al., 2018b; Munassar et
al., 2022) and LUMIA (Monteil and Scholze, 2021). Both
inversions employ pre-computed sensitivities of atmospheric mole fractions
to surface fluxes, so-called source-weight functions or “footprints”, via
two Lagrangian transport models at regional scales, and they make use of the
two-step inversion approach established by Rödenbeck et al. (2009) to provide the lateral boundary conditions. The regional atmospheric
transport models were used at a horizontal resolution of 0.25∘. The
impacts of both global and regional models were compared by analysing
the differences in space and time.
Section 2 presents detailed descriptions of the inversion setups, the
transport models, and the a priori fluxes used. The observational stations that
provide CO2 dry mole fraction data are described within the Methods section as well.
We introduce the results obtained from eight inversions in Sect. 3. The
results are discussed and interpreted through a spatial and temporal
analysis of the differences between the elements of inversions in Sect. 4.
Finally, Sect. 5 highlights a few concluding remarks on the impacts of
regional transport, boundary conditions, and inversion setups on CO2
estimates in the inverse modelling.
Methods
An atmospheric tracer inversion framework is mainly made up of transport
model, data source for boundary conditions (in case of regional inversions),
datasets of atmospheric mole fractions, and surface flux fields. In this
study, several inversion runs differing in atmospheric transport models are
conducted using two tracer inversion systems, CSR and LUMIA (see Table 2).
The default CSR inversion system utilizes pre-calculated footprints from the
Stochastic Time-Inverted Lagrangian Transport (STILT) model (Lin et al.,
2003) at the regional domain and the TM3 model at the global scale,
applying the two-step scheme inversion approach
(Rödenbeck et al., 2009), to provide the far-field
contributions to the regional domain. In the default setup of the inversion
system LUMIA, the footprints are pre-calculated using the
Lagrangian particle dispersion model FLEXPART
(Pisso et al., 2019), and the far-field
contributions are calculated using the global transport model TM5 in a
separate global inversion run, applying the two-step scheme inversion as
well. These default configurations in both systems constitute the base
cases. We strive to restrict the differences in the inversion runs to the
targeted components, i.e. regional transport, boundary conditions, and the
inversion systems, so as to outline the impact of each suite. That is, input
data such as measurements of CO2 dry mole fraction and the a priori
fluxes, used as constraints based on Bayesian inference, are identical for all
runs. We exchangeably make use of the four combinations of transport model
components, the regional and global models, in the two inversion systems.
The impacts were evaluated using forward model runs to quantify the
differences in CO2 concentrations (simulated with prior fluxes) and
inversion runs to quantify the magnitude of differences in the flux space.
The inversion setups and implementation are explained in the
comparison protocol (Sect. 2.6).
Inversion framework
In the following description, we remind the reader about the basic principles
of the inversion schemes. For detailed information about the mathematical
schemes, the reader is referred to Rödenbeck (2005) for CSR and to
Monteil and Scholze (2021) for LUMIA. Both systems rely on the
Bayesian inference that accounts for observations and a priori knowledge to
regularize the solution of the ill-posed inverse problem where a unique
solution does not exist due to the spatial scarcity of observations.
Therefore, the optimal state vector (x) is searched for in the Bayesian
formalism by minimizing the cost function J(x) that is typically composed of the
observational constraint term Jc(x) and the a priori flux constraint term Jb(x):
Jx=Jcx+Jbx,
where
2Jbx=12x-xbTB-1x-xb,3Jcx=12H(x)-yTQ-1H(x)-y.
The a priori flux uncertainty defined in the covariance matrix
B limits the departure of the control vector
(x) to the a priori flux vector (xb).
Similarly, the observational constraint is weighted by the observational
covariance matrix Q that contains the so-called
model–data mismatch error, including uncertainty of measurement,
representativeness, and transport. This uncertainty is assigned to the
diagonal of the matrix Q for the respective sites based
on the ability of the transport model to represent the atmospheric
circulation at such locations. H(x) represents the
atmospheric transport operator (i.e. calculated by STILT and FLEXPART in
our inversions) that determines the relation between fluxes and the modelled
tracer concentration, which corresponds spatially and temporally to a given
vector of measurements y. Following the gradient descent method, a
variational algorithm is applied iteratively to reach the best convergence
(global minimum) of the cost function that satisfies the optimal solution of
the control vector. The default configurations for constructing the
covariance matrices of a priori uncertainty are slightly different in CSR and
LUMIA. A priori flux uncertainty is assumed to be around 0.47 PgC yr-1
over the full domain of Europe derived from the global uncertainty (2.80 PgC) assumed in the CarboScope global inversion for the annual biogenic
fluxes (Rödenbeck et al., 2003). In CSR, this
uncertainty is uniformly distributed spatially and temporally in a way that
the annual uncertainty aggregated over the entire domain should arrive at
the same value. The uncertainty structure is fit to a hyperbolic decay
function in space (Eq. 4) and to an exponential function (Eq. 5) for the
temporal decay as explained in Kountouris et al. (2015).
4rs=11+sds,5rt=e-tdt.
The correlation length scales ds and dt applied to flux uncertainties are chosen
to be 66.4 km spatially and 30 d temporally, respectively, following
Kountouris et al. (2018a) and
Munassar et al. (2022). The spatial length in the
zonal direction is set to be longer than that in the meridional direction by
a factor of 2 (anisotropic), owing to larger spatial climate variability in
the meridional as compared to zonal direction.
The spatio-temporal shape of the a priori uncertainty in LUMIA is computed in a
way that each control vector comprises weekly uncertainty calculated as the
standard deviation of NEE based on weekly flux variance; however, LUMIA
agrees on the overall annually aggregated flux uncertainty over the entire
domain with CSR. A Gaussian function of the spatial correlation decay (Eq. 6) is applied to the a priori uncertainty structure with a spatial length
scale of 500 km,
rs=e-sds2,
whereas the effective temporal decay was set to 30 d (same as in CSR).
Given the difference in the spatial correlation decay of the a priori
uncertainty, LUMIA is set to draw larger flux corrections in a broader
radial area where stations exist following the Gaussian decay with a longer
length scale compared to the hyperbolic decay in CSR. In turn, the
hyperbolic function has a larger impact in the further radial distances than
the Gaussian function does, regardless of the longer spatial scale assumed
with the Gaussian decay in a factor of around 7.5 in comparison with the
hyperbolic decaying function.
Atmospheric transport models
Surface sensitivities are calculated using the STILT (Lin et al., 2003) and
FLEXPART (Pisso et al., 2019) models at
a horizontal resolution of 0.25∘ and hourly temporal resolution. Both
models simulate the transport of air masses via releasing an ensemble of
virtual particles at the locations of stations. The virtual particles are
transported backward in time and driven by meteorological fields obtained
from the European Centre for Medium-Range Weather Forecasts (ECMWF). STILT
particles are transported 10 d backward in time and forced by forecasting
data obtained from the high-resolution implementation of the Integrated
Forecasting System (IFS HRES). For the FLEXPART model in standard operation,
particles are followed for 15 d backward in time driven by ERA-5
reanalysis data. To keep the consistency with STILT footprints, the backward
time of FLEXPART footprints was limited to 10 d in the inversions. After
this backward time integration, the particles are assumed to leave the
domain, even though a large number of particles are expected to escape after
a few days. To better represent air sampling in the mixed layer, day-time
observations are considered, except for mountain stations where night-time
observations are used instead (Geels et al., 2007). To ensure best mixing
conditions, temporal windows were considered for simulating CO2 dry
mole fractions over stations as explained in Sect. 2.4 (Table 1). In
addition, release heights of particles are taken as the highest sampling
level above ground at each measurement site. For high-altitude receptors,
such as mountains, a correction height is used in STILT in a way that the
actual elevation of the station can be represented in the corresponding
vertical model level (Munassar et al., 2022). In
FLEXPART, the elevation above sea level is taken as the model sampling
height.
Three components of prior and prescribed surface-to-atmosphere fluxes of
CO2 are obtained from (1) biogenic terrestrial fluxes, (2) ocean fluxes,
and (3) anthropogenic emissions and kept identical in both systems. Prior net
terrestrial CO2 exchange fluxes, net ecosystem exchange (NEE), are
calculated using the diagnostic biogenic model Vegetation Photosynthesis and
Respiration Model (VPRM) (Mahadevan et al., 2008). VPRM calculates NEE at
hourly temporal and 0.25∘ spatial resolutions, and it provides a
partitioning of the net flux into gross ecosystem exchange (GEE) and
ecosystem respiration. Data obtained from remote sensing provided through
the MODIS instrument and meteorological parameters from ECMWF drive both
quantities of the light-dependent GEE and the light-independent ecosystem
respiration. The model parameters were also optimized against eddy
covariance data selected within the global FLUXNET site network across
Europe in 2007 (Kountouris et al., 2015). For more details on the VPRM
model, the reader is referred to Mahadevan et al. (2008).
Ocean fluxes are taken from Fletcher et al. (2007), who provide
climatological fluxes at a spatial resolution of 5∘×4∘, remapped to 0.25∘ to be compatible with the biosphere model fluxes.
In addition, anthropogenic emissions are taken from the EDGAR_v4.3 inventory and are updated to recent years according to British
Petroleum (BP) statistics of fossil fuel consumption, and they are distributed
spatially and temporally based on fuel type, category, and country-specific
emissions, using the COFFEE approach (Steinbach et al.,
2011). The emissions are remapped to a 0.25∘ spatial grid and to
an hourly temporal resolution.
Biogenic terrestrial fluxes are optimized in the inversions, while the ocean
fluxes and anthropogenic emissions are prescribed, given the better
knowledge about their spatial and temporal distribution in comparison with
the heterogeneity, variability, and uncertainty of the biogenic fluxes.
Moreover, in the absence of observational constraints that help discriminate
the contributions from the three categories, we chose to prescribe the ocean
fluxes and anthropogenic CO2 emissions. This is also justified by the
fact that the observation sites are located in areas where the biospheric
flux influence is expected to dominate the variability of CO2
concentration, but it means that errors in the fossil fuel or ocean fluxes might
be compensated by the inversions, resulting in changes in the posterior
NEE.
Observations
Measurements of CO2 dry mole fractions are collected through ICOS,
NOAA, and pre-ICOS stations across the domain of Europe provided by Drought 2018 Team and ICOS Atmosphere Thematic Centre (2020). In total, datasets from 44 stations are used covering the domain of
Europe in 2018, in which a maximum number of stations is present compared to
the other years. Regarding model–data mismatch errors, in LUMIA a weekly value of
1.5 ppm is assumed for all sites, except for the Heidelberg site where 4 ppm
was assumed due to the anthropogenic influence from the neighbourhood. Table 1 denotes the weekly values of uncertainty used in CSR for the corresponding
sites. The uncertainty for the surface sites is inflated to 2.5 ppm as a
slight difference to LUMIA. The inflation of uncertainty from weekly to
hourly values is basically calculated by multiplying weekly errors by 7×n (where n refers to the number of hours in the daily measurements
used in the inversion). The observations are mostly assimilated as hourly
continuous measurements and are taken from the highest level, avoiding
large vertical gradients near the surface that are hard to represent in the
transport models. Model error in representing observations in the planetary boundary layer (PBL) is
expected to be largest when the PBL is shallow. Therefore, for most sites,
we considered data only when the PBL was expected to be well developed,
i.e. during the afternoon, local time (LT). The exception is at high-altitude sites, which tend to sample the free troposphere during night
(Kountouris et al., 2018b). The assimilated windows are
reported in Table 1.
Boundary conditions
Far-field contributions of CO2 concentrations (originating from sources
outside of the regional domain) are taken from global inversions. As default
setups of the global runs, the Eulerian transport model TM3 is used in the
CarboScope global inversion at 5∘ (long) × 4∘ (lat),
while TM5-4DVAR (Transport Model 5 – Four Dimensional Variational model) is
used to provide boundary conditions to LUMIA using the global transport
model TM5 at 6∘ (long) × 4∘ (lat) (Babenhauserheide et
al., 2015; Monteil and Scholze, 2021). Both inversion systems apply the
two-step scheme inversion, explained in Rödenbeck et al. (2009), in which a global inversion is first used to estimate CO2
fluxes globally (based on observations inside and outside Europe). In a
second step, the global transport model is used to estimate the influence of
European CO2 fluxes on European CO2 observations. That regional
influence is then subtracted from the total concentration to obtain a
time series of the far-field influence directly at the locations of the
observation sites. This prevents introducing biases by passing concentration
fields from one model to another. For detailed information about the
approach methodology, the reader is referred to Rödenbeck et
al. (2009).
Comparison protocol
The results of the study are based on eight variants of inversions differing
in global and regional transport models, as well as in inversion systems, as
explained in Table 2. This implies that the two inversion systems (CSR and
LUMIA) make use of two regional transport models (STILT and FLEXPART) and
two global transport models (TM3 and TM5), which represent the boundary
conditions (background) calculated from two global inversions. Hereafter,
the identifier codes (see corresponding column in Table 2) will be used to
refer to the individual runs within the inversion ensemble. For instance, to
highlight the impact of regional transport models, we compare the inversions
that only differ in regional transport models, regardless of the inversion
system or boundary conditions used, such as CS3 and CF3 or LS5 and LF5.
Similarly, we use the same specifications of transport models (indicated
through the identifier codes) for the forward runs to outline the
differences in CO2 concentrations simulated using prior fluxes with
different transport models. In this case, using a different system should not
result in discrepancies as long as prior fluxes remain identical. In terms
of system-to-system comparison, the impact of flux uncertainty should be
taken into account as the prior error structure is specific for each
inversion system. With that said, this has been investigated by conducting
additional tests in CSR and LUMIA using identical uncertainties with flat
shape and Gaussian correlation decay.
Results
Estimates of the regional biosphere–atmosphere fluxes over the domain of
Europe are calculated using CSR and LUMIA for 2018 from an ensemble of eight
inversions as listed in Table 2. Generally, all the inversions showed that
the estimates of NEE are constrained by the atmospheric data as can be seen
from the positive flux corrections made by the inversions in comparison with
the a priori fluxes calculated from the biosphere flux model VPRM, which
obviously overestimates CO2 uptake, specifically during the growing
season (Fig. 1a). This is also obvious in the ensemble-averaged annual
estimates of posterior fluxes -0.29 PgC versus -1.49 PgC in the a priori fluxes
(Fig. 1b). However, the spread among posterior estimates is still
relatively large, ranging between -0.72 and 0.20 PgC yr-1 for the annual
estimates, which is larger than the a priori uncertainty of 0.47 PgC yr-1.
Likewise, the mean standard deviations of the monthly estimates over the
ensemble of inversions is 0.72 PgC yr-1. The largest deviations occur
between inversions that differ by the regional transport models (e.g. CS3
versus CF3 or LS5 versus LF5). In addition, the seasonal amplitude was
found to be different between the STILT and FLEXPART inversions. The
STILT-based inversions led to a larger amplitude of posterior NEE than the
FLEXPART-based inversions.
Panel (a) refers to a posteriori monthly NEE estimated using eight
inversions, including a priori NEE shown in black, with CSR (solid
lines) and LUMIA (dashed lines), and panels (b) denotes the corresponding
annually aggregated fluxes. Orange and red colours correspond to TM3, and
dark or light blue correspond to TM5. Orange and light blue colours refer to STILT, and red
and dark blue refer to FLEXPART.
In terms of spatial distributions, the base cases of CSR and LUMIA
inversions, i.e. CS3 and LF5 (default configurations of both systems),
exhibit good agreement in predicting smaller uptake of CO2 compared to
the a priori fluxes (Fig. 2a–c). The magnitude of flux corrections
suggests additional sources inferred from the atmospheric signal, as
shown in the innovations of fluxes (Fig. 2d, e). Major corrections
are obtained over western and southern Europe where the inversions point to
an overestimation of the CO2 uptake by the prior biogenic fluxes. The
weak annual uptake of CO2 in 2018 was exceptional and caused by the
drought episode in Europe (Bastos et al., 2020; Rödenbeck et al.,
2020; Thompson et al., 2020), which even turned some areas in central,
northern, and western Europe into a net source of CO2. The
discrepancies between CS3 and LF3 noticed in the innovations, e.g. in
northern France, the Netherlands, and south-eastern UK, are attributable to the
combination of differences in regional transport models, lateral boundaries,
and system configurations.
Panels (a)–(c) show the spatial distributions of annual NEE estimated
with the base inversions CS3 and LF5, as well as their prior. Panels (d) and (e)
depict the innovations of fluxes calculated for the inversions CS3 and LF5.
Green circles denote the locations of observational sites.
In the following, we will focus on separating and quantifying the
contributions of such differences caused by each driver.
Impact of mesoscale transport
Inversions that differ in the regional transport models (STILT and FLEXPART)
demonstrate the largest differences in posterior fluxes, resulting in a
relative contribution of about 61 % of the total differences compared to
the boundary conditions and inversion systems. The differences in monthly
estimates of NEE calculated with CS3 and CF3 inversion setups that vary in
regional transport models are shown in Fig. 3a (“transport”).
Additionally, the discrepancies caused by transport have an obvious seasonal
pattern. The differences between CS3 and CF3 peak in November and June,
reaching 2.11 and -1.82 PgC yr-1, respectively. The best agreement
between both inversions is obtained during the transitional months (August
and April) with differences of -0.10 and -0.18 PgC yr-1,
respectively. This might be attributed to the decline of the net flux
magnitude during these months.
Differences in optimized fluxes (a) and prior concentrations
(b) calculated with the regional transport models STILT and FLEXPART
(CS3-CF3) and background provided through TM3 and TM5 (CS3-CS5). “system”
refers to the differences between CSR and LUMIA inversion for optimized
fluxes (CS5-LS5).
Furthermore, we assessed the impact of atmospheric transport in the
simulations of CO2 concentrations, because this directly translates into
differences in the optimized fluxes. These simulations were calculated using
the total components of prior fluxes (biosphere, ocean, and fossil fuel
emissions) with STILT and FLEXPART in forward model runs to sample the
atmospheric concentrations at hourly time steps at the station locations
across the site network. Note that since all runs use identical prior
fluxes, it does not matter for the differences whether the prior fluxes were
precise enough to reproduce the true concentration or not. Figure 3b (“transport”) illustrates the monthly differences in the forward
simulations between STILT and FLEXPART averaged over all observational
stations. Similarly to the discrepancies in the optimized fluxes, the
differences in the forward simulations demonstrate a dominant impact of the
regional transport model, preserving the same temporal pattern as seen in the
flux differences but with opposite signs. The absolute difference ranges
from 0.39 to 4.37 ppm when computed for the monthly means throughout all the
sites. Geels et al. (2007) even found a larger spread up to 10 ppm when
calculated with five transport models over 10 stations distributed across
Europe. The notably large difference reported in that study is likely
attributed to the large discrepancies in the model configurations,
especially regarding the horizontal resolution and vertical levels used. The
harmonized configurations used in STILT and FLEXPART lead to a reasonably
consistent representation of the atmospheric variability at synoptic and
diurnal timescales. The largest differences are observed during November and
May with -4.37 and 3.60 ppm, respectively. On the other hand, the smallest
differences were found to be -0.39, -0.42, and 0.56 ppm during September,
April, and August, respectively. These results suggest a maximum impact of
the mesoscale transport during the growing season and winter, while the
impact converges to the minimum during transitional months such as May and
September. Overall, the differences in posterior fluxes are consistent in
the timing with the differences in the simulated concentrations computed
using the prior fluxes.
Further diagnostics of model–data mismatches are provided in the
Supplement, indicating the performances of STILT and FLEXPART
with respect to the observations using prior and posterior fluxes across the
site network at hourly, weekly, and yearly time steps (see Fig. 1S and Table 1S).
In terms of the spatial discrepancies in annual flux estimates, using STILT
generally leads to predicting a larger sources of CO2 in the regional
inversions, in particular over central Europe and the UK compared to using
FLEXPART (Fig. 4, “diff: transport”). In turn, inversions using FLEXPART
suggest less uptake over northern Italy, Switzerland, and south-eastern
France. However, this impact refers to a spatial pattern of transport
differences that might be caused either by meteorological data or by
problematic sites that are hard to represent by transport models. Some areas
such as north-western Italy exhibit a persistent impact over time as shown
in Fig. 4 (“SD: transport”), which shows the standard deviation of monthly
differences calculated for the CS3 and CF3 inversions. In terms of temporal
variations, the inversions performed with different regional transport
models indicate larger monthly flux variations in comparison with those
differing in global models and inversion systems (see Fig. 4, “SD:
background” and “SD: system”).
Panels (a)–(c) indicate differences in annual posterior NEE estimated
with STILT and FLEXPART models, referred to as “transport” (CS3-CF3); TM3
and TM5 are referred to as “background” (CS3-CS5); and CSR and LUMIA are referred
to as “system” (CF3-LF3). Panels (d)–(f) demonstrate the standard deviations
of the corresponding monthly differences.
Figure 5 shows the spatial flux differences together with differences in
prior concentrations simulated using STILT and FLEXPART during June and
December. Note that the differences in NEE, to a large extent, agree in
their spatial patterns with the differences in prior concentrations
calculated over the station network. In addition, there are notably
particular areas that exhibit opposite signs of the spatial impact in the
differences in posterior fluxes and prior concentrations such as western
Europe during June and northern Europe during December. One important
difference between STILT and FLEXPART is that the STILT model has higher
sensitivities during summer than FLEXPART, while the opposite holds true
during winter. However, there are exceptions at individual sites such as
Weybourne (WAO) in the UK and Ispra (IPR) in Italy, indicating either
difficult terrains that cannot be well represented by the models or real
synoptic features that are resolved by one model but not by the other. The
differences in forward simulations are inversely manifested in the posterior
flux differences as large surface sensitivities result in smaller posterior
flux corrections and vice versa. In this case, STILT computes higher
surface sensitivities than FLEXPART in June; therefore, the CS3 inversion
needs to adjust the prior fluxes less to fit the observations. On the
contrary, a weaker uptake is suggested by the STILT inversion during December
over Europe, except for the abovementioned areas around northern Italy and
south-eastern France. The differences appeared to be larger during the
months of growing season and winter, following the seasonal amplitude of
CO2.
Spatial differences of posterior NEE estimated from the inversions
CS3 and CF3 with STILT and FLEXPART transport models during June and
December; filled circles indicate the differences in prior concentrations at
the locations of sites (horizontal legend explains the magnitude of
differences).
Impact of lateral boundary conditions
The differences in lateral boundary conditions were found to account for
about 27 % of the total differences resulting from the regional transport,
lateral boundaries, and systems. This is a non-negligible contribution,
albeit smaller than the regional transport contribution. The impact of using
different far-field contributions was analysed by assessing the differences
in the posterior NEE estimated with CS3 and CS5 inversions, which use
boundary conditions from the global inversions CarboScope and TM5-4DVAR,
respectively. Figure 3 (“background”) shows consistent differences over
time between these inversion estimates aggregated over the entire domain of
Europe. Larger flux corrections are suggested by CS5 than by CS3. This is
because the global TM3-based inversion predicts higher influence at the
lateral boundaries than the global TM5-based inversion does. Discrepancies
in the monthly posterior fluxes between CS3 and CS5 inversions amount to a
range of 0.11 to 0.64 PgC yr-1 and absolute differences with a mean of
0.40 PgC yr-1. Monthly-mean differences in CO2 concentrations
throughout all sites simulated using TM3 and TM5 boundary conditions were
found to range from 0.17 to 0.93 ppm with a mean of 0.55 ppm.
The distributions of spatial differences of posterior fluxes indicate a
homogeneous impact across the full domain of Europe (Fig. 4, “diff:
background”). Likewise, the standard deviations of the monthly posterior
fluxes obtained from CS3-CS5 (”SD: background”) denote flat temporal
variations throughout all the grid cells. These findings confirm the results
obtained in Fig. 3 (“background”). This impact is consistent in space and
time, with coherent deviation over all months, and is therefore expected to
not affect the seasonal and interannual variability.
Impact of inversion systems
CS3 and LF5 differ by more than their regional transport and boundary
conditions. In particular, the uncertainties are, by default, set up
differently in CSR and LUMIA. The two systems optimize a different set of
variables (weekly NEE offsets in LUMIA and 3-hourly NEE in CSR). Here we
compare CS5 and LS5, which differ by their inversion systems but not by
their transport model and boundary conditions. The differences in flux
estimates between CS5 and LS5 inversions amount to 12 % relative to the
total differences, including that caused by the mesoscale transport and
lateral boundaries. This impact is, however, dependent upon system
configurations, in particular the way the prior flux uncertainty is
prescribed. The absolute monthly differences between CS5 and LS5 range
between 0.06 and 0.56 PgC yr-1 with a mean of 0.15 PgC yr-1
(Fig. 3, “system”). This demonstrates the smallest differences amid
inversions in comparison with the transport and lateral boundary
differences, which yielded absolute monthly means of 1.27 and 0.40 PgC yr-1, respectively. The differences peaked during May, June, and
November, while the differences remained rather small during the rest of the
year. LS5 infers -6.42 and 2.39 PgC yr-1 during June and December,
respectively, which is higher than CS5 estimates by 0.33 and 0.07 PgC yr-1. Generally, LS5 predicts slightly larger CO2 releases
compared to CS5, which is partially due to differences in how uncertainties
are assumed in both systems.
The impact of uncertainty definition is quantitatively assessed by
using identical uncertainties for model–data mismatch as well as for prior
fluxes in both CSR and LUMIA. The spatial flux corrections (innovation of
fluxes) shown in Fig. 8 denote quite good agreement between CSR and LUMIA
estimates. In this experiment, the differences in June and December
decreased to 0.23 and 0.04 PgC yr-1, respectively, in comparison with
the corresponding differences obtained from the default configurations of
both systems. That is to say, the impact of uncertainty definition alone
amounts to 0.09 and 0.03 PgC yr-1 in June and December, respectively,
leading to approximately 30 % and 50 % of the overall system-to-system
differences. The rest of the differences may be attributed to differences in
the convergence of the cost function to reach the minimum values.
The spatial differences shown in Fig. 4 “diff: system” alternate between
positive and negative differences over the domain (but these tend to
compensate when aggregating the flux estimates over the full domain). It
should be noted that the inversion systems mainly differ in the definition
of the shape and structure of the prior uncertainty. Therefore, applying
different structure and magnitude of prior flux uncertainty in the
inversions may inflate the error in CO2 flux estimates over the
underlying regions in the domain, in particular if the spatial differences
do not cancel out. In addition, the corresponding standard deviations of
monthly estimates (“SD: system”) show large temporal variations,
specifically over areas that have large spatial differences. The spatial
results indicate that the impact of inversion systems should not be
neglected, especially at national and subnational scales.
Discussion
The regional inversions computed over Europe showed that posterior NEE is
largely derived from the atmospheric signal. The seasonality of posterior
NEE, inferred from the atmospheric signal, is strongly impacted by
differences in the representation of atmospheric transport. Given the
identical priors and observational datasets used in the inversions, using
different mesoscale transport models leads to 61 % of the differences in
posterior fluxes in comparison with 27 % and 12 % of the differences
caused by the use of different boundary conditions and different inversion
systems, respectively. In agreement with these results, Schuh et al. (2019) also found a large impact of mesoscale transport on estimating
CO2 fluxes. Hence, any error in the atmospheric transport is translated
into posterior fluxes as flux corrections. For instance, CS3 and LS3 suggest
annual CO2 flux budgets of -0.20 and -0.72 PgC, respectively,
indicating a difference of 0.51 PgC in the annual flux budget. This
difference is even larger than the prior flux uncertainty (0.47 PgC). The
transport also showed a large impact on flux seasonality, leading to a
difference of 49 % relative to the mean seasonal cycle. However, Schuh
et al. (2019) found smaller differences, amounting to about 10 %–15 % of the
mean seasonal cycle. Unlike the regional transport model error, the impact
of boundary conditions does not show any striking seasonality and thus can
be thought of as a bias in dry mole fractions. The consistency of the
lateral boundary impact over time and space is in agreement with results of
lateral boundary uncertainties assessed by Chen et al. (2019) using four
different global transport models, albeit over a different domain.
Therefore, such an impact may be dealt with as a constant correction in
mixing ratios before performing the regional inversions, which are potentially
site-specific corrections. But there should be a reference for these
corrections, e.g. taking the most robust model that has been
validated against observations or simply a factor of the relative mean of
the relevant models/approaches. Although the inversion systems showed the
smallest differences in CO2 flux estimates, the specification of the
control vector (regarding the construction of covariance matrices) that
devises the flux correction can result in larger differences, specifically
in the spatial flux patterns.
The large number of stations within central and western Europe leads to a
strong observational constraint that is reflected in the spatially optimized fluxes over that area. Therefore, large spatial differences between the
inversions are pronounced around areas where stations exist, precisely for
grid cells that have non-zero footprints. The large temporal variations
indicate a systematic error that possibly arises from the transport models
themselves as well as from meteorological forcing data. Additionally,
systematic differences between transport models occur due to discrepancies
in representing vertical mixing and horizontal and vertical resolution of
the models (Peylin et al., 2002). Gerbig et al. (2008) found
large discrepancies in derived mixing heights between meteorological
analysis from ECMWF and radiosonde data, which reached about 40 % for the
day-time and about 100 % for the nocturnal boundary layer. The vertical
mixing in tracer dispersion models was found to result in a significant
variability in methane emission estimations (up to a factor of 3) given the
same meteorology as investigated by Karion et al. (2019).
Drivers of STILT–FLEXPART differences
Although STILT and FLEXPART are run at the same spatio-temporal resolution,
employing similar schemes to parametrize the atmospheric motion unresolved
by meteorological forcing data such as turbulence, and similar diagnostics
to determine mixing heights, they still exhibit large spatial and temporal
differences. A first assumption was that the differences between STILT and
FLEXPART could be caused by differences in the calculation of mixing height.
However, we did not find a correlation between the differences in mixing
heights, calculated with the two models, and the differences in prior
concentrations (Fig. 6). This finding concludes that the discrepancies in
representing mixed layer heights do not explain the major differences in
simulated CO2 concentrations nor the differences in footprints.
Scatter plot of differences of prior concentrations and mixing
heights calculated with STILT and FLEXPART models (i.e. STILT-FLEXPART on
the x and y axes). Red lines indicate the slopes.
The second assumption was that differences in the forcing data of
meteorological products might lead to the discrepancies in both models,
given that STILT uses meteorological parameters from IFS HRES, while
FLEXPART uses the ERA-5 reanalysis. Results in Fig. 7, “meteo”, indicate that
using different meteorological data results in pronounced differences when
the FLEXPART model was forced by operational forecast data instead of the ERA-5
reanalysis. These differences notably occur during the time of net CO2
release, corresponding to quite small differences during the time of growing
season. This, however, only explains a small part of the overall differences
(shown in Fig. 7, “base”) that dominate all the months except August and
September. In a previous study, Liu et al. (2011) concluded
that uncertainties in meteorological fields lead to a significant
contribution to the total transport error, as well as to an underestimation
of the vertical turbulent mixing even when the same circulation model and
mixing parameterizations were used to reconstruct vertical mixing from a
single meteorological analysis. Tolk et al. (2008) also
found meteorology to be a key driver of representation error, which varies
spatially and temporally. They indicated that a large contribution to
representation error is caused by unresolved model topography at coarse
spatial resolution during night, while convective structures, mesoscale
circulations, and the variability of CO2 fluxes dominate during
day-time. Deng et al. (2017) found that assimilating meteorological
observations such as wind speed and wind direction in transport models
significantly improved the model performances, achieving an uncertainty
reduction of about 50 % in wind speed and direction, especially when
measurements in the mixed layer were assimilated. Nonetheless, they
concluded that the differences in CO2 emissions reached up to 15 % at
local-scale corrections after inversion and were limited to 5 % for the
total emissions integrated across the regional domain of interest. These
results refer to the limited impact of meteorological data. Note however
that the main aim of this experiment was to test whether differences in
driving meteorological data could explain the differences between STILT and
FLEXPART, but we are not assessing the overall impact of meteorological
uncertainties. Doing so would in particular require testing non-ECMWF
meteorological products.
Differences in prior concentration simulated at LIN with STILT and
FLEXPART using different configurations. “s_layer”, yellow
line, refers to the difference calculated with STILT using two assumptions
of defining the surface layer height, once with the default as 0.5 of the
mixed layer and once with 100 m as used in FLEXPART; “meteo”, red line,
indicates the differences calculated with FLEXPART using two different types
of meteorological data, IFS (the STILT default) and ERA-5; “model”, blue
line, denotes the differences calculated with STILT and FLEXPART, given
identical meteorological data (IFS) and surface layer height (100 m);
“base”, black line, refers to the base configurations of STILT and
FLEXPART encompassing all possible differences between models – i.e. (1) STILT with IFS forecasting data and a surface layer height as 0.5 times that of the
mixed layer height and (2) FLEXPART with ERA-5 reanalysis and the surface
layer height of 100 m.
Furthermore, we tested the possible impact of surface layer heights (the
height up to which particles are sensitive to the fluxes) that may affect
the particle dispersion, provided that STILT relies on the assumption of
defining the surface layer as a half of the mixed layer height, while in
FLEXPART it is defined as a fixed height of 100 m (these are default
configurations of the models). In this experiment, STILT was run with a
surface layer height of 100 m, so the impact of the surface layer on
CO2 simulations is outlined by the comparison with another run using
the default configurations of STILT. The differences in simulated CO2
concentrations due to differences in the surface layer were found to be
quite small (Fig. 7, “s_layer”) and, therefore, can be
negligible in both magnitude and temporal pattern compared to the overall
differences. However, varying the models STILT and FLEXPART with identical
meteorological data and identical surface layer leads to the largest
differences, in particular during the growing season months and winter
months (Fig. 7, “model”). As a result, model-to-model differences largely
affect the simulations of CO2 concentrations and are likely originating
from the transport model schemes. It is clearly noticeable that the overall
differences combine the underlying differences of “model”, “meteo”, and
“s_layer” and are yielded as the arithmetic summation of
this partitioning.
Innovation of fluxes calculated from CSR and LUMIA using identical
uncertainties of prior flux and measurements. The uncertainty flux shape was
flat and the decaying spatial correlation was fit to a Gaussian function with
500 km scale. FLEXPART and TM5 models were used in this experiment.
How do our results explain the range of uncertainties reported in scientific
literature?
To shed more light on the drivers of differences in optimized CO2
fluxes, we analyse the spread in our inversions in line with the spreads in
other inversion estimates that were reported in two previous studies over
the same domain of Europe. Figure 9 shows the spreads amid the three
studies: (1) eight inversions conducted in our results denoted as
“Ensemble”, (2) six inversions of the EUROCOM experiment (denoted as “EUROCOM”) done
by Monteil et al. (2020), and (3) five inversions of the drought study by Thompson et al. (2020), focusing
on analysing the 2018 drought impact on NEE, denoted as “Drought”. Note
that in “EUROCOM” and “Drought”, the tracer inversions differed in the
atmospheric regional transport models, the definition of boundary
conditions, the definition of control vector, the selection of atmospheric
datasets, and the a priori fluxes. These differences are expected to span a
large range of uncertainty sources in the posterior NEE. The climatological
monthly estimates of NEE were averaged over “EUROCOM” inversion members
for the respective years 2006–2015, except for one inversion (NAME), which
was limited to 2011–2015. “Ensemble” and “Drought” were confined to the
analysis year of 2018. The monthly NEE estimates were calculated for all
ensembles as the average over their respective inversion members. The annual
mean of NEE estimated with “EUROCOM”, “Ensemble”, and “Drought”
amounts to -0.19, -0.29, and -0.05 PgC with standard deviations of 0.34, 0.29, and 0.46 PgC, respectively.
Comparison of monthly NEE estimates calculated as the mean of six
inversions taken from Monteil et al. (2020), denoted as “EUROCOM”; eight
inversion members conducted in our study (setups listed in Table 2),
denoted as “Ensemble”; and five inversions used in Thompson et al. (2020)
for the 2018 drought study, denoted as “Drought”. The error bars refer to
the spreads (min/max) over the respective members amid each ensemble of
inversions.
The spreads amid each ensemble of inversions are illustrated by the min and
max values bounded around the mean on the error bars (Fig. 9). The monthly
mean of NEE estimates shows a good consistency in all the ensembles. The
spreads are also relatively comparable, albeit variable over months. For
instance, “EUROCOM” and “Drought” exhibit larger spreads during the
growing season (April–August), while “Ensemble” has a larger spread in the
rest of the months – i.e. during winter. Note that all ensembles experience
large spreads during June and May. Although the participating inversions to
“EUROCOM” and “Drought” had different configurations, the spreads were
not largely different from our inversion spreads. This implies that the use
of different atmospheric transport models could account for a large fraction
of differences in posterior fluxes, although differences in the definition
of uncertainty covariance matrices and lateral boundary conditions likely
contribute as well. Moreover, the discrepancies in “EUROCOM” and
“Drought” estimates are expected to be partially caused by using different
atmospheric datasets in the inversion systems. Munassar et al. (2022) found
that posterior fluxes can be more sensitive to changing the number of
stations than changing the prior flux models.
Conclusions
Estimating atmospheric tracer fluxes through inverse modelling systems has
been widely used, in particular for targeting the major greenhouse gases (GHGs) to improve the
quantification of natural (both terrestrial and oceanic) sources and sinks.
Here, an analysis of differences in posterior fluxes of CO2 was carried
out using inversion systems deploying different regional transport models.
The difference between minimum and maximum spreads for annually integrated
fluxes was found to be 0.92 PgC yr-1 for the ensemble range of 0.20 and
-0.72 PgC yr-1, with a mean estimate of -0.29 PgC yr-1 calculated
over the full domain of Europe in 2018. We tested the regional transport,
the boundary conditions, and the inversion systems. The regional transport
accounts for the largest part of the discrepancies in the optimized fluxes
as well as in the estimation of CO2 concentration. Temporal and spatial
differences in posterior fluxes are consistent with the differences in
simulated CO2 concentration sampled with STILT and FLEXPART over the
station network. They demonstrate a spatial pattern over certain areas
during June and December, suggesting rather systematic differences between
STILT and FLEXPART. The differences in the regional transport are mainly
caused by the transport schemes, while meteorological forcing data partially
contribute to these differences, especially during the months in which net
release of CO2 occurs. However, the differences in CO2 simulations
did not show large sensitivities to other parameters such as the way the
surface layer height (maximum altitude considered sensitive to the fluxes in
Lagrangian models) and the mixing height are defined. In addition, the
global transport models used in the global inversions that provide the far-field contributions to the regional domain are responsible for small but
non-negligible differences in the inversion estimates. These differences
appeared to be homogeneous spatially and temporally, which can be considered
as bias-like. The differences arising from using different inversion systems
integrated over the entire domain of Europe were on the contrary rather
small, once differences such as the transport model and the uncertainties
are controlled for. However, such an impact is partially a result of
applying different structure and shape in the prior flux uncertainty, while
the rest may be attributed to differences in the cost function convergence
to reach the minimum. This reflects the importance of the way the
uncertainty is prescribed in the tracer inversion systems.
The divergence in CO2 flux estimates resulting from swapping the
regional transport model emphasizes the need for further evaluation of
atmospheric transport models in order to improve the performance of the
models. At the same time, it is important to realistically account for the
transport errors in the tracer inversions. Errors in meteorology parameters
assimilated in transport models as forcing data should also be accounted for
explicitly, potentially through making use of an ensemble of meteorology
data to estimate such errors. Despite the non-negligible difference between
inversion systems, this study indicates the importance of following a common
inversion protocol when reporting flux estimates from different inversion
frameworks.
Code and data availability
The simulations of the ensemble of inversions (a posteriori NEE calculated using CSR and LUMIA) and their respective prior fluxes can be accessed from 10.18160/QE4G-TP7T (Munassar and Monteil, 2023). The codes used to create the figures can be made available upon request to the corresponding author. The atmospheric datasets of CO2 dry mole fractions are available at the ICOS Carbon Portal and can be accessed from 10.18160/ERE9-9D85 (Drought 2018 Team and ICOS Atmosphere Thematic Centre, 2020).
The supplement related to this article is available online at: https://doi.org/10.5194/acp-23-2813-2023-supplement.
Author contributions
SM and GM designed the study. CG, MS, UK, and KUT gave valuable suggestions in frequent discussions that helped improve the design and the structure of the study. SM wrote the paper and performed the simulations of CSR. GM performed the simulations of LUMIA. CG prepared and provided the fluxes of VPRM, and FTK processed the anthropogenic emission datasets. CR designed and develops the code of CSR. All authors revised the paper and edited the text.
Competing interests
At least one of the (co-)authors is a member of the editorial board of
Atmospheric Chemistry and Physics. The peer-review process was guided by an
independent editor, and the authors also have no other competing interests
to declare.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The authors thank Mathias Göckede for his valuable comments on the
manuscript in the internal review. Saqr Munassar, Christoph Gerbig, Christian Rödenbeck, and Frank-Thomas Koch acknowledge the
computational support of Deutsches Klimarechenzentrum (DKRZ) where the CSR
inversion system is implemented. The computations of LUMIA were enabled by
resources provided by the Swedish National Infrastructure for Computing
(SNIC) at NSC (National Supercomputer Centre), partially funded by the Swedish Research Council through
grant agreement no. 2018-05973. Marko Scholze and Guillaume Monteil acknowledge support from the three Swedish strategic research areas ModElling the Regional and Global Earth system (MERGE), the e-science collaboration (eSSENCE), and Biodiversity and Ecosystems in a Changing Climate (BECC).
The authors acknowledge the provision of the atmospheric dataset of CO2 dry mole fractions compiled by ICOS ATC (Atmospheric Thematic Centre).
Financial support
This research has been supported by the H2020 projects VERIFY (grant no. 776810) and CoCO2 (grant no. 958927), as well as by BMBF through the ITMS-M project under contract 01LK2102A.The article processing charges for this open-access publication were covered by the Max Planck Society.
Review statement
This paper was edited by Susannah Burrows and reviewed by Jia Jung and one anonymous referee.
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